An Australian Greens motion calling for the terms of reference of a proposed Royal Commission to be expanded to cover violence, abuse and neglect of older Australians and disabled people in institutional and residential settings has been blocked.

Australian Greens Disability Rights spokesperson Senator Jordon Steele-John succeeded in securing the votes of the entire crossbench but the motion was ultimately voted down by the Labor and Liberal parties.

After writing to the Commissioner in relation to child abuse claims in Australian immigration detention centres, The Australian Greens welcome news that the Royal Commission into Institutional Responses to Child Sexual Abuse is considering allegations of abuse against children within the detention network.

"Refugee children are already extremely vulnerable and the fact that some of them have been subjected to further abuse and assault is sickening and must be exposed" Greens spokesperson on Immigration, Senator Sarah Hanson-Young said.

The Australian Greens have called on Tony Abbott to initiate a Royal Commission into the conditions and management of Australia's offshore detention camps, which led to the death of an Iranian refugee while in Australia's care on Manus Island.

"The tragedy of a refugee killed while in Australia's care should be the final nail in the coffin for Labor and the Abbott government's morally bankrupt and cruel offshore processing regime," Australian Greens Leader, Senator Christine Milne said.